What is the derivative of (e^x/(e^x-1)) ?

The derivative of (e^x/(e^x-1)) is -(e^x)/((e^x-1)^2)

What is the first derivative of (e^x/(e^x-1)) ?

The first derivative of (e^x/(e^x-1)) is -(e^x)/((e^x-1)^2)

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Popular >

\frac{d}{d x} (\frac{e ^{x}}{e ^{x} - 1})

- \frac{e ^{x}}{( e ^{x} - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{e ^{x} - 1})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{x} ) ( e ^{x} - 1 ) - \frac{d}{d x} ( e ^{x} - 1 ) e ^{x}}{( e ^{x} - 1 ) ^{2}}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (e^{x} - 1) = e^{x}

= \frac{e ^{x} ( e ^{x} - 1 ) - e ^{x} e ^{x}}{( e ^{x} - 1 ) ^{2}}

Simplify

\frac{e ^{x} ( e ^{x} - 1 ) - e ^{x} e ^{x}}{( e ^{x} - 1 ) ^{2}} : - \frac{e ^{x}}{( e ^{x} - 1 ) ^{2}}

= - \frac{e ^{x}}{( e ^{x} - 1 ) ^{2}}

\int ln (x^{2} + x) d x

\frac{\partial}{\partial x} (z arctan (y x))

\int \frac{1}{4 e ^{- 3 x} + e ^{3 x}} d x

\int_{- 2}^{1} (x - 6 ∣ x ∣) d x

x \to 0 lim (- x^{4})

What is the derivative of (e^x/(e^x-1)) ?
The derivative of (e^x/(e^x-1)) is -(e^x)/((e^x-1)^2)
What is the first derivative of (e^x/(e^x-1)) ?
The first derivative of (e^x/(e^x-1)) is -(e^x)/((e^x-1)^2)